A natural history of networks: Modeling higher-order interactions in geohistorical data

Paleobiologists are increasingly employing network-based methods to analyze the complex data retrieved from geohistorical records, including stratigraphic sections, sediments, and fossil collections. However, the lack of a common framework for designing, performing, evaluating, and communicating these studies, leads to issues of reproducibility and communicability. The high-dimensional geohistorical data also raises questions about the limitations of standard network approaches, which assume independent interactions between pairs of components. Higher-order network models better suited for the complex relational structure of the geohistorical data provide an opportunity to overcome these challenges. These models can represent temporal and spatial constraints inherent to the biosedimentary record and describe higher-order interactions, capturing more accurate biogeographical, biostratigraphic, and macroevolutionary patterns. Here we describe how to use the Map Equation framework for designing higher-order network models of geohistorical data, address some practical decisions involved in modeling complex dependencies, and discuss critical methodological and conceptual issues that currently make it difficult to compare results across studies in the growing body of network-based paleobiology research. We illustrate different higher-order network representations and models, including multilayers, hypergraphs, and varying Markov times models, using case studies on gradient analysis, bioregionalization, and macroevolution, and delineate future research directions for current challenges in the emerging field of network paleobiology.